Finite Group Databasebeta

← #21445618

Subgroups — #21445618

Order 7808.

284 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519785C211yesmaximal, characteristic
2#16839744C211yesmaximal, characteristic
3#16839735C211yesmaximal, characteristic
4#16839720C211yesmaximal, characteristic, complemented
5#16839718C211yesmaximal, characteristic, complemented
6#16839533C211yesmaximal, characteristic, complemented
7C61×#344C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519785—21no—
10#14519785—21no—
11#14519785—21no—
12#14519785—21no—
13C2×#11758194C2211yescharacteristic
14C2×#11758189C412yescomplemented
15C22×#92418C2211yescharacteristic
16C2×C8×D61C412yescomplemented
17#14519736C2211yescharacteristic
18#14519695C412yescomplemented
19#14519693C412yescomplemented
20#14519691C414yes—
21#14519688—21no—
22#14519687—21no—
23C4×#92418—21no—
24C8×Dic61—21no—
25C2×M16×C61C2211yescharacteristic
26C2×M16×C61C2211yescharacteristic
27#117×C61C2211yescharacteristic
28C22×C4×C61C2311yescharacteristic
29C2×C22⋊D61C2×C412yes—
30#11758222—21no—
31#11758222—21no—
32#11758222—21no—
33#11758222—21no—
34C2×D244C2×C411yescharacteristic
35C2×C4×D61C2×C412yes—
36C2×Dic122C2×C411yescharacteristic
37M16×C61—21no—
38M16×C61—21no—
39M16×C61—21no—
40M16×C61C2×C412yes—
41C2×C8×C61—21no—
42C2×C8×C61C2×C412yes—
43C4⋊C4×C61—21no—
44C22⋊C4×C61C2×C412yes—
45C42×C61—21no—
46C22⋊Dic61C2×C412yes—
47C4⋊Dic61—21no—
48C4×Dic61—21no—
49#11758194—21no—
50#11758194C2×C412yes—
51C2×#92418—21no—
52C2×#92418C2×C411yescharacteristic
53C2×#92418C2×C411yescharacteristic
54C2×#92418D411yescharacteristic
55C2×#92418D411yescharacteristic
56C2×#92418D411yescharacteristic
57C2×#92418D411yescharacteristic
58#11758189—22no—
59#11758189—22no—
60C8×D61—22no—
61C8×D61—22no—
62C23×C61C22×C411yescharacteristic
63C22×D61C4212yes—
64C2×C4×C61—22no—
65C2×C4×C61C22×C411yescharacteristic
66C2×C4×C61C22×C411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61#4111yescharacteristic
70C2×C4×C61#4111yescharacteristic
71C22⋊D61—22no—
72C22⋊D61—22no—
73C2×Dic61—22no—
74C2×Dic61C4212yes—
75D244—21no—
76D244—21no—
77C4×D61—22no—
78C4×D61—22no—
79Dic122—21no—
80Dic122—21no—
81C8×C61—22no—
82C8×C61—22no—
83#92418—22no—
84#92418C22⋊C411yescharacteristic
85#92418C22⋊C411yescharacteristic
86#92418C22⋊C411yescharacteristic
87#92418C22⋊C411yescharacteristic
88C22×C61—41no—
89C22×C61C2×C4211yescharacteristic
90C22×C61C4×D411yescharacteristic
91C22×C61C4×D411yescharacteristic
92C2×D61—22no—
93C2×D61—42no—
94C4×C61—42no—
95C4×C61C2×C22⋊C411yescharacteristic
96C4×C61#11711yescharacteristic
97C4×C61C4×D411yescharacteristic
98C4×C61C4×D411yescharacteristic
99Dic61—22no—
100Dic61—42no—
101#1757—611nomaximal, Sylow
102C2×C61—21no—
103C2×C61—21no—
104C2×C61—21no—
105C2×C61C4×C22⋊C411yescharacteristic
106D61—42no—
107C2×#131—611no—
108#413—611no—
109#410—611no—
110#405—611no—
111#405—611no—
112#344—611no—
113#344D6111yescharacteristic, complemented
114C61#175711yescharacteristic, complemented, Sylow
115C2×#41—611no—
116#131—1221no—
117#131—1221no—
118#131—1221no—
119#131—1221no—
120C2×M16—612no—
121C2×M16—611no—
122C2×M16C2×D6111yescharacteristic
123C2×M16C2×D6111yescharacteristic
124C22×C8—611no—
125C22×C8—612no—
126#117—611no—
127#117C2×D6111yescharacteristic
128#101—612no—
129#100—612no—
130#99—614no—
131#97—1221no—
132#97—1221no—
133C4×C8—1221no—
134C4×C8—1221no—
135#41—1221no—
136#41—1221no—
137#41—1221no—
138#41—1221no—
139C2×Q8—611no—
140C2×D4—612no—
141C2×D4—611no—
142C22×C4—612no—
143C22×C4C22×D6111yescharacteristic
144M16—21no—
145M16—21no—
146M16—21no—
147M16—612no—
148M16—1222no—
149M16—1222no—
150M16—1221no—
151M16C4×D6112yes—
152C2×C8—21no—
153C2×C8—611no—
154C2×C8—611no—
155C2×C8—611no—
156C2×C8—611no—
157C2×C8—611no—
158C2×C8—611no—
159C2×C8—1222no—
160C2×C8—1222no—
161C2×C8—1221no—
162C2×C8C4×D6112yes—
163C4⋊C4—21no—
164C4⋊C4—1221no—
165C22⋊C4—612no—
166C22⋊C4C4×D6112yes—
167C42—21no—
168C42—1221no—
169C23—612no—
170C23C2×C4×D6111yescharacteristic
171Q8—1221no—
172Q8—1221no—
173D4—1222no—
174D4—1222no—
175D4—1221no—
176D4—1221no—
177C2×C4—22no—
178C2×C4—612no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4C2×C4×D6111yescharacteristic
183C2×C4C2×C4×D6111yescharacteristic
184C2×C4D4×D6111yescharacteristic
185C2×C4D4×D6111yescharacteristic
186C2×C4#1175822411yescharacteristic
187C2×C4#1175822611yescharacteristic
188C8—22no—
189C8—22no—
190C8—611no—
191C8—611no—
192C8—611no—
193C8—611no—
194C8—1222no—
195C22—41no—
196C22—1222no—
197C22—2442no—
198C22C42×D6111yescharacteristic
199C22#1451973711yescharacteristic
200C22#1451973911yescharacteristic
201C4—42no—
202C4—1222no—
203C4—2442no—
204C4C22⋊C4×D6111yescharacteristic
205C4#1451973511yescharacteristic
206C4#1451973711yescharacteristic
207C4#1451973911yescharacteristic
208C2—21no—
209C2—21no—
210C2—21no—
211C2—2442no—
212C2#1683960911yescharacteristic
subgroupG/H
centerC4C22⋊C4×D61
commutatorC22×C61C2×C42
FrattiniC22×C4C22×D61
FittingC61×#344C2
socleC2×C61C4×C22⋊C4
hypercenter#344D61
hypocenterC61#1757
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #16839720C2semidirect
5. #16839718C2semidirect
6. #16839533C2semidirect
7. C61×#344C2semidirect
14. C2×#11758189C4semidirect
16. C2×C8×D61C4semidirect
18. #14519695C4semidirect
19. #14519693C4semidirect
113. #344D61semidirect
114. C61#1757semidirect